具有豐富頻譜資源的毫米波 (Millimeter wave, mmWave)
通訊系統被視為下一時代無線通訊系統的潛力技術，在高頻
段傳輸可獲得每秒十億位元的高資料速率，但同時也引入了
巨大的傳輸損耗使通訊品質大幅下降，為了確保良好的通訊
品質，高指向性的波束成型 (Beamforming) 被視為毫米波通訊
系統中不可或缺的關鍵技術，因此精準的訊號出發角 (Angle
of Departure, AoD)、入射角 (Angle of Arrival, AoA) 及路徑增益顯得特別重要。特別是移動通訊 (mobile communications) 場景，環
境的些許變化導致傳送端與接收端的波束錯位，使接收訊號
的品質明顯下降，因此角度與路徑增益的估計與追蹤成為毫米波通訊系統的核心研究主題。本論文考慮單一使用者多輸
入多輸出正交分頻多工 (Multiple-Input Multiple-Output Orthogonal
Frequency-Division Multiplexing , MIMO-OFDM) 的均勻線性陣列
(Uniform Linear Array, ULA) 天線架構，並假設傳送端與接收端使
用全連接混合波束成型 (full connection hybrid beamforming) 架構，
在初始階段，利用分層波束訓練 (hierarchical beam training) 對空間
進行粗掃描 (coarse search) 及細掃描 (fine search)，使獲得最佳的
波束匹配，並假設傳送端與接收端的波束中心角為初始估計的訊
號出發角、入射角，而初始路徑增益由最小平方法 (least squares)
求出，接著利用正交匹配追蹤 (Orthogonal Matching Pursuit, OMP)
取得混合波束成型架構之預編碼器 (precoder) 與結合器 (combiner)
權重。我們採用多路徑二維通道 (multi-path two-dimensional (2D)
channel) 為通道環境，並提出基於決策反饋 (Decision Feedback) 無
跡卡爾曼濾波器 (Unscented Kalman Filter) 自適應演算法，不需要
UKF 波束追蹤前導序列 (preamble) 也能克服時變的傳送端與接收
端波束匹配，達到高效率低時間成本的波束追蹤 (beam tracking)，
並利用模擬結果進行性能分析與討論。

Millimeter-Wave (mmWave) communication system with abundant spectrum resources is regarded as the potential technology of the
next-generation wireless communication system. The high data rate of
one gigabit per second can be obtained in high-frequency band transmission, but it also introduces a huge transmission loss that greatly reduces communication quality. In order to ensure good communication
quality, beamforming with high directivity is regarded as an indispensable key technology in the mmWave communication system. Therefore,
the precise signal Angle of Departure ( AoD), Angle of Arrival (AoA),
and path gain are critical. Especially in mobile communications scenarios, slight changes in the environment cause the beams at the transmitter and receiver to be misaligned, which significantly degrades the quality of
the received signal. Therefore, the estimation and tracking of angle and
path gains have become the core research topics of the mmWave communication systems. This paper considers a single-user Multiple-Input with high efficiency and low time overhead. finally, the simulation results are used for performance analysis and discussion.
Multiple-Output Orthogonal Frequency-Division Multiplexing (MIMOOFDM) Uniform Linear Array (ULA) antenna architecture. It assumes
that the full connection hybrid beamforming architecture is used for both
the transmitter and receiver. In the initial stage, hierarchical beam training is used to perform coarse search and fine search on the angle space, to
obtain the best beam matching, and to assume that the beam center angles
of the transmitter and receiver end are the initially estimated signal AoD
and AoA, respectively, and the initial path gain is obtained by the Least
Squares (LS) method, Orthogonal Matching Pursuit(OMP) obtains the
precoder and combiner weights of the hybrid beamforming architecture.
We use a multi-path two-dimensional (2D) channel as the channel environment, and propose an adaptive algorithm for the decision feedback
based Unscented Kalman Filter(UKF), which does not require UKF beam
tracking preambles and can also overcome the time-varying beam matching between the transmitter and the receiver, and achieve beam tracking

[1] Z. Pi and F. Khan, “An introduction to millimeter-wave mobile
broadband systems,” IEEE Communications Magazine, vol. 49,
no. 6, pp. 101–107, 2011.
[2] T. S. Rappaport, S. Sun, R. Mayzus, H. Zhao, Y. Azar, K. Wang,
G. N. Wong, J. K. Schulz, M. Samimi, and F. Gutierrez, “Millimeter
wave mobile communications for 5g cellular: It will work!” IEEE
Access, vol. 1, pp. 335–349, 2013.
[3] S. Hur, T. Kim, D. J. Love, J. V. Krogmeier, T. A. Thomas, and
A. Ghosh, “Millimeter wave beamforming for wireless backhaul
and access in small cell networks,” IEEE Transactions on Communications, vol. 61, no. 10, pp. 4391–4403, 2013.
[4] T. S. Rappaport, Y. Xing, G. R. MacCartney, A. F. Molisch, E. Mellios, and J. Zhang, “Overview of millimeter wave communications
for fifth-generation (5g) wireless networks—with a focus on propagation models,” IEEE Transactions on Antennas and Propagation,
vol. 65, no. 12, pp. 6213–6230, 2017.
[5] “Ieee draft amendment to ieee standard for information technology–
telecommunications and information exchange between systems–
local and metropolitan area networks–specific requirements–part
15.3: Wireless medium access control (mac) and physical layer
(phy) specifications for high rate wireless personal area networks
(wpans): Amendment 2: Millimeter-wave based alternative physical layer extension,” IEEE Unapproved Draft Std P802.15.3c/D08,
Mar 2009, 2009.
[6] “Ieee standard for information technology–telecommunications and
information exchange between systems–local and metropolitan area
networks–specific requirements-part 11: Wireless lan medium access control (mac) and physical layer (phy) specifications amendment 3: Enhancements for very high throughput in the 60 ghz band,”IEEE Std 802.11ad-2012 (Amendment to IEEE Std 802.11-2012,
as amended by IEEE Std 802.11ae-2012 and IEEE Std 802.11aa2012), pp. 1–628, 2012.
[7] I. Ahmed, H. Khammari, A. Shahid, A. Musa, K. S. Kim,
E. De Poorter, and I. Moerman, “A survey on hybrid beamforming techniques in 5g: Architecture and system model perspectives,”
IEEE Communications Surveys Tutorials, vol. 20, no. 4, pp. 3060–
3097, 2018.
[8] O. E. Ayach, S. Rajagopal, S. Abu-Surra, Z. Pi, and R. W. Heath,
“Spatially sparse precoding in millimeter wave mimo systems,”
IEEE Transactions on Wireless Communications, vol. 13, no. 3, pp.
1499–1513, 2014.
[9] R. W. Heath, N. González-Prelcic, S. Rangan, W. Roh, and A. M.
Sayeed, “An overview of signal processing techniques for millimeter wave mimo systems,” IEEE Journal of Selected Topics in Signal
Processing, vol. 10, no. 3, pp. 436–453, 2016.
[10] A. Alkhateeb, O. El Ayach, G. Leus, and R. W. Heath, “Channel
estimation and hybrid precoding for millimeter wave cellular systems,” IEEE Journal of Selected Topics in Signal Processing, vol. 8,
no. 5, pp. 831–846, 2014.
[11] L. Dai, X. Gao, S. Han, I. Chih-Lin, and X. Wang, “Beamspace
channel estimation for millimeter-wave massive mimo systems with
lens antenna array,” in 2016 IEEE/CIC International Conference on
Communications in China (ICCC), 2016, pp. 1–6.
[12] A. Alkhateeb, G. Leus, and R. W. Heath, “Compressed sensing based multi-user millimeter wave systems: How many measurements are needed?” in 2015 IEEE International Conference
on Acoustics, Speech and Signal Processing (ICASSP), 2015, pp.
2909–2913.
[13] T. Kim and D. J. Love, “Virtual aoa and aod estimation for sparse
millimeter wave mimo channels,” in 2015 IEEE 16th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2015, pp. 146–15.

[14] X. Xin and Y. Yang, “Robust beam tracking with extended kalman
filtering for mobile millimeter wave communications,” in 2019
Computing, Communications and IoT Applications (ComComAp),
2019, pp. 172–177.
[15] C. Lin, G. Y. Li, and L. Wang, “Subarray-based coordinated beamforming training for mmwave and sub-thz communications,” IEEE
Journal on Selected Areas in Communications, vol. 35, no. 9, pp.
2115–2126, 2017.
[16] S. Noh, M. D. Zoltowski, and D. J. Love, “Multi-resolution codebook and adaptive beamforming sequence design for millimeter
wave beam alignment,” IEEE Transactions on Wireless Communications, vol. 16, no. 9, pp. 5689–5701, 2017.
[17] J. He, T. Kim, H. Ghauch, K. Liu, and G. Wang, “Millimeter wave
mimo channel tracking systems,” in 2014 IEEE Globecom Workshops (GC Wkshps), 2014, pp. 416–421.
[18] S. Shaham, M. Kokshoorn, M. Ding, Z. Lin, and M. Shirvanimoghaddam, “Extended kalman filter beam tracking for millimeter
wave vehicular communications,” in 2020 IEEE International Conference on Communications Workshops (ICC Workshops), 2020, pp.
1–6.
[19] C. Zhang, D. Guo, and P. Fan, “Tracking angles of departure and
arrival in a mobile millimeter wave channel,” in 2016 IEEE International Conference on Communications (ICC), 2016, pp. 1–6.
[20] S. Jayaprakasam, X. Ma, J. W. Choi, and S. Kim, “Robust beamtracking for mmwave mobile communications,” IEEE Communications Letters, vol. 21, no. 12, pp. 2654–2657, 2017.
[21] B. Liu, W. Tan, H. Hu, and H. Zhu, “Hybrid beamforming for
mmwave mimo-ofdm system with beam squint,” in 2018 IEEE 29th Annual International Symposium on Personal, Indoor and Mobile
Radio Communications (PIMRC), 2018, pp. 1422–1426.
[22] Z. Sha, Z. Wang, and S. Chen, “Harmonic retrieval based baseband channel estimation for millimeter wave ofdm systems,” IEEE
Transactions on Vehicular Technology, vol. 68, no. 3, pp. 2668–
2681, 2019.
[23] H. Van Trees, Optimum Array Processing: Part IV of Detection,
Estimation, and Modulation Theory, ser. Detection, Estimation, and
Modulation Theory. Wiley, 2002.
[24] P. Bello, “Characterization of randomly time-variant linear channels,” IEEE Transactions on Communications Systems, vol. 11,
no. 4, pp. 360–393, 1963.
[25] H. Xu, V. Kukshya, and T. Rappaport, “Spatial and temporal characteristics of 60-ghz indoor channels,” IEEE Journal on Selected
Areas in Communications, vol. 20, no. 3, pp. 620–630, 2002.
[26] V. Va, H. Vikalo, and R. W. Heath, “Beam tracking for mobile millimeter wave communication systems,” in 2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP), 2016,
pp. 743–747.
[27] J. Lim, H.-M. Park, and D. Hong, “Beam tracking under highly
nonlinear mobile millimeter-wave channel,” IEEE Communications
Letters, vol. 23, no. 3, pp. 450–453, 2019.
[28] J. Meditch, Stochastic Optimal Linear Estimation and Control, ser.
Electronics Series. McGraw-Hill, 1969.
[29] M. Pätzold, Mobile Fading Channels, ser. Online access: EBSCO
Computers & Applied Sciences Complete. Wiley, 2002.
[30] L. Liu, H. Ju, X. Fang, Y. Long, and R. He, “Systematic design of
radar detection under ieee 802.11ad framework,” in 2021 IEEE 94th
Vehicular Technology Conference (VTC2021-Fall), 2021, pp. 1–5.
[31] Z. Guo, X. Wang, and W. Heng, “Millimeter-wave channel estimation based on 2-d beamspace music method,” IEEE Transactions on
Wireless Communications, vol. 16, no. 8, pp. 5384–5394, 2017.
[32] H. Li, M. Li, Q. Liu, and A. L. Swindlehurst, “Dynamic hybrid beamforming with low-resolution pss for wideband mmwave
mimo-ofdm systems,” IEEE Journal on Selected Areas in Communications, vol. 38, no. 9, pp. 2168–2181, 2020.
[33] J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Transactions on
Information Theory, vol. 53, no. 12, pp. 4655–4666, 2007.
[34] L. Rebollo-Neira and D. Lowe, “Optimized orthogonal matching
pursuit approach,” IEEE Signal Processing Letters, vol. 9, no. 4,
pp. 137–140, 2002.
[35] T. Kailath, A. Sayed, and B. Hassibi, Linear Estimation, ser.
Prentice-Hall information and system sciences series. Prentice
Hall, 2000. [Online]. Available: https://books.google.com.tw/
books?id=zNJFAQAAIAAJ
[36] E. Wan and R. Van Der Merwe, “The unscented kalman filter for
nonlinear estimation,” in Proceedings of the IEEE 2000 Adaptive
Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373), 2000, pp. 153–158.
[37] S. G. Larew and D. J. Love, “Adaptive beam tracking with the unscented kalman filter for millimeter wave communication,” IEEE
Signal Processing Letters, vol. 26, no. 11, pp. 1658–1662, 2019.
[38] F. W. Vook, A. Ghosh, E. Diarte, and M. Murphy, “5g new radio:
Overview and performance,” in 2018 52nd Asilomar Conference on
Signals, Systems, and Computers, 2018, pp. 1247–1251.